Question

An experimental rocket designed to land upright falls freely from a height of 2.88 102 m, starting at rest. At a height of 95.9 m, the rocket's engines start and provide constant upward acceleration until the rocket lands. What acceleration is required if the speed on touchdown is to be zero? (Neglect air resistance.)

Answer 1

Vf^2=Vi^2+2Anet*d where
Anet=-9.8+a

Now vi, figure from change of PE
1/2 m vi^2=mg*(-288)-ma(-95.9)
solve for vi.

Then,
vf^2=0=Vi^2+2*-9.8*-95.9+2a*-95.9
solve for a

Note Vi is negative, but when squared, postive. a should end up to be positive. Notice and think out why I put a - on the 288, on the 9.8, and on the 95.6.

Answer 2

What acceleration is required if the speed on touchdown is to be zero?